Detectives launched an investigation following the incident on Tuesday night near to the A406 in Wanstead.
Two men were arrested on suspicion of arson and attempted murder on Thursday, the Metropolitan Police said.
Local reports in the Ilford Recorder newspaper said that a tent in which two men were sleeping was set alight, prompting them to flee into the road to seek help.
The victims were taken to hospital, where one died and the other remains in critical condition. Both were believed to be sleeping rough, police told HuffPost UK.
Police have yet to confirm the identities of the men or those arrested.
Detective Sergeant Ian Valentine, said: “We are working hard to establish the circumstances that led to this fatal fire and we believe the public can assist us with our investigation.
“We know that after the fire started, two men came out onto the A406 in an attempt to seek assistance from passing drivers.
“Anyone who believes they may have seen these two people on the verge or stopped to speak to them is urged to contact us. In particular we are keen to hear from anyone who has any relevant dashcam footage.”
Anyone with information is asked to call 101 with CAD reference 9090/18JUN.